When Do Item Response Function and Mantel-Haenszel Definitions of Differential Item Functioning Coincide?

1990 ◽  
Vol 15 (3) ◽  
pp. 185 ◽  
Author(s):  
Rebecca Zwick
Keyword(s):  
Differential Item Functioning ◽  
Item Response ◽  
Response Function ◽  
Item Functioning ◽  
Item Response Function

When Do Item Response Function and Mantel-Haenszel Definitions of Differential Item Functioning Coincide?

1990 ◽  
Vol 15 (3) ◽  
pp. 185-197 ◽  
Author(s):  
Rebecca Zwick
Keyword(s):  
Differential Item Functioning ◽  
Item Response ◽  
Response Function ◽  
Response Functions ◽  
Local Independence ◽  
Matching Criterion ◽  
Demographic Groups ◽  
Item Functioning ◽  
Item Response Function ◽  
The Rasch Model

A test item is typically considered free of differential item functioning (DIF) if its item response function is the same across demographic groups. A popular means of testing for DIF is the Mantel-Haenszel (MH) approach. Holland and Thayer (1988) showed that, under the Rasch model, identity of item response functions across demographic groups implies that the MH null hypothesis will be satisfied when the MH matching variable is test score, including the studied item. This result, however, cannot be generalized to the class of items for which item response functions are monotonic and local independence holds. Suppose that all item response functions are identical across groups, but the ability distributions for the two groups are stochastically ordered. In general, the population MH result will show DIF favoring the higher group on some items and the lower group on others. If the studied item is excluded from the matching criterion under these conditions, the population MH result will always show DIF favoring the higher group.

A Generalized Formula for the Mantel-Haenszel Differential Item Functioning Parameter

1999 ◽  
Vol 24 (3) ◽  
pp. 293-322 ◽  
Author(s):  
Louis A. Roussos ◽  
Deborah L. Schnipke ◽  
Peter J. Pashley
Keyword(s):  
Differential Item Functioning ◽  
Item Response ◽  
Item Difficulty ◽  
Difficulty Level ◽  
Population Parameter ◽  
Simulation Studies ◽  
Item Functioning ◽  
The Difference ◽  
Item Response Function ◽  
Two Parameter

The present study derives a general formula for the population parameter being estimated by the Mantel-Haenszel (MH) differential item functioning (DIF) statistic. Because the formula is general, it is appropriate for either uniform DIF (defined as a difference in item response theory item difficulty values) or nonuniform DIF; and it can be used regardless of the form of the item response function. In the case of uniform DIF modeled with two-parameter-logistic response functions, the parameter is well known to be linearly related to the difference in item difficulty between the focal and reference groups. Even though this relationship is known to not strictly hold true in the case of three-parameter-logistic (3PL) uniform DIE the degree of the departure from this relationship has not been known and has been generally believed to be small By evaluating the MH DIF parameter, we show that for items of medium or high difficulty, the parameter is much smaller in absolute value than expected based on the difference in item difficulty between the two groups. These results shed new light on results from previous simulation studies that showed the MH DIF statistic has a tendency to shrink toward zero with increasing difficulty level when used with 3PL data.

A Bifactor Multidimensional Item Response Theory Model for Differential Item Functioning Analysis on Testlet-Based Items

2011 ◽  
Vol 35 (8) ◽  
pp. 604-622 ◽  
Author(s):  
Hirotaka Fukuhara ◽  
Akihito Kamata
Keyword(s):  
Item Response Theory ◽  
Differential Item Functioning ◽  
Item Response ◽  
Estimation Method ◽  
Multidimensional Item Response Theory ◽  
Multidimensional Item Response ◽  
Response Theory ◽  
Data Set ◽  
Detection Rates ◽  
Item Functioning

A differential item functioning (DIF) detection method for testlet-based data was proposed and evaluated in this study. The proposed DIF model is an extension of a bifactor multidimensional item response theory (MIRT) model for testlets. Unlike traditional item response theory (IRT) DIF models, the proposed model takes testlet effects into account, thus estimating DIF magnitude appropriately when a test is composed of testlets. A fully Bayesian estimation method was adopted for parameter estimation. The recovery of parameters was evaluated for the proposed DIF model. Simulation results revealed that the proposed bifactor MIRT DIF model produced better estimates of DIF magnitude and higher DIF detection rates than the traditional IRT DIF model for all simulation conditions. A real data analysis was also conducted by applying the proposed DIF model to a statewide reading assessment data set.

scholarly journals Determining differential item functioning and its effect on the test scores of selected pib indexes, using item response theory techniques

2001 ◽  
Vol 27 (2) ◽  
Author(s):  
Pieter Schaap
Keyword(s):  
Item Response Theory ◽  
Differential Item Functioning ◽  
Item Response ◽  
Test Scores ◽  
Response Theory ◽  
South Africans ◽  
Test Characteristics ◽  
Potential Index ◽  
Item Functioning

The objective of this article is to present the results of an investigation into the item and test characteristics of two tests of the Potential Index Batteries (PIB) in terms of differential item functioning (DIP) and the effect thereof on test scores of different race groups. The English Vocabulary (Index 12) and Spelling Tests (Index 22) of the PIB were analysed for white, black and coloured South Africans. Item response theory (IRT) methods were used to identify items which function differentially for white, black and coloured race groups. Opsomming Die doel van hierdie artikel is om die resultate van n ondersoek na die item- en toetseienskappe van twee PIB (Potential Index Batteries) toetse in terme van itemsydigheid en die invloed wat dit op die toetstellings van rassegroepe het, weer te gee. Die Potential Index Batteries (PIB) se Engelse Woordeskat (Index 12) en Spellingtoetse (Index 22) is ten opsigte van blanke, swart en gekleurde Suid-Afrikaners ontleed. Itemresponsteorie (IRT) is gebruik om items te identifiseer wat as sydig (DIP) vir die onderskeie rassegroepe beskou kan word.

scholarly journals Differential item functioning of the Boston Naming Test in cognitively normal African American and Caucasian older adults

2009 ◽  
Vol 15 (5) ◽  
pp. 758-768 ◽  
Author(s):  
OTTO PEDRAZA ◽  
NEILL R. GRAFF-RADFORD ◽  
GLENN E. SMITH ◽  
ROBERT J. IVNIK ◽  
FLOYD B. WILLIS ◽  
...  
Keyword(s):  
African American ◽  
Item Response Theory ◽  
Differential Item Functioning ◽  
Item Response ◽  
Group Performance ◽  
Response Theory ◽  
Boston Naming Test ◽  
Item Functioning ◽  
The Impact ◽  
Naming Test

AbstractScores on the Boston Naming Test (BNT) are frequently lower for African American when compared with Caucasian adults. Although demographically based norms can mitigate the impact of this discrepancy on the likelihood of erroneous diagnostic impressions, a growing consensus suggests that group norms do not sufficiently address or advance our understanding of the underlying psychometric and sociocultural factors that lead to between-group score discrepancies. Using item response theory and methods to detect differential item functioning (DIF), the current investigation moves beyond comparisons of the summed total score to examine whether the conditional probability of responding correctly to individual BNT items differs between African American and Caucasian adults. Participants included 670 adults age 52 and older who took part in Mayo’s Older Americans and Older African Americans Normative Studies. Under a two-parameter logistic item response theory framework and after correction for the false discovery rate, 12 items where shown to demonstrate DIF. Of these 12 items, 6 (“dominoes,” “escalator,” “muzzle,” “latch,” “tripod,” and “palette”) were also identified in additional analyses using hierarchical logistic regression models and represent the strongest evidence for race/ethnicity-based DIF. These findings afford a finer characterization of the psychometric properties of the BNT and expand our understanding of between-group performance. (JINS, 2009, 15, 758–768.)

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